Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 06 Apr 2011 12:40:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Apr/06/t1302093514czmxhjrxlwyhilw.htm/, Retrieved Thu, 09 May 2024 13:29:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120351, Retrieved Thu, 09 May 2024 13:29:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords KDGP1W52
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [IKO opgave 5 opdr...] [2011-04-06 12:40:43] [93d78dde8d64c5a73537ad1fcc88d508] [Current]
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Dataseries X:
5939520,00
89948768,00
80953652,00
85942882,00
8944937,00
82975432,00
24940816,00
21973899,00
37950221,00
45949881,00
85950373,00
48960313,00
81954506,00
24960419,00
65973338,00
22950513,00
54963528,00
90995659,00
91967517,00
28999053,00
96990529,00
38979852,00
81496957,00
74982424,00
70976192,00
90990000,00
12998850,00
92986156,00
67994976,00
91022206,00
87992489,00
421022698,00
11018942,00
79100042,00
65996442,00
51000620,00
12996871,00
44994249,00
99996135,00
91977037,00
63974211,00
15998036,00
65974265,00
33984410,00
45939098,00
67935827,00
66921032,00
89911836,00
71890975,00
72880342,00
28871286,00
41844334,00
82847667,00
24871401,00
3867451,00
99896846,00
41890361,00
45884264,00
69884586,00
95896400,00
39904491,00
81900399,00
27909863,00
88900470,00
89917101,00
2945005,00
4934411,00
61957264,00
31946515,00
3938309,00
52933321,00
21947613,00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120351&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120351&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean61236226.16666676166783.369390579.9300109147045
Geometric Mean44817948.0129479
Harmonic Mean25561026.4747938
Quadratic Mean80311579.5574312
Winsorized Mean ( 1 / 24 )56790335.65277783563956.925633515.9346301983386
Winsorized Mean ( 2 / 24 )56789545.90277783563075.0485883415.9383524423033
Winsorized Mean ( 3 / 24 )56709953.61111113534418.9525475316.0450570157326
Winsorized Mean ( 4 / 24 )56705008.05555563513322.337146816.1399958825316
Winsorized Mean ( 5 / 24 )56711617.29166673440781.7578532316.4821895960789
Winsorized Mean ( 6 / 24 )56800357.79166673395089.0031374316.7301527998757
Winsorized Mean ( 7 / 24 )56991730.88888893358952.5031678416.9671142521782
Winsorized Mean ( 8 / 24 )56886916.22222223343658.1143825917.0133770487855
Winsorized Mean ( 9 / 24 )57258496.09722223275251.330727817.48216863849
Winsorized Mean ( 10 / 24 )58084040.26388893134605.801112118.5299345274234
Winsorized Mean ( 11 / 24 )57928979.06944443110660.4219155818.6227267564523
Winsorized Mean ( 12 / 24 )58086470.23611113083583.0118729618.8373298245763
Winsorized Mean ( 13 / 24 )58432346.61111113028540.8857484519.2938939296078
Winsorized Mean ( 14 / 24 )58249189.47222222997875.7686506519.4301545385386
Winsorized Mean ( 15 / 24 )58064110.72222222970191.7265995819.5489436598414
Winsorized Mean ( 16 / 24 )58265739.16666672804991.3764100420.7721633858418
Winsorized Mean ( 17 / 24 )58490973.11111112770351.6015086321.1131948303093
Winsorized Mean ( 18 / 24 )57781052.36111112664298.2545230421.68715618194
Winsorized Mean ( 19 / 24 )58525139.06944442543324.0927404623.0112785218745
Winsorized Mean ( 20 / 24 )58843120.73611112427475.3730124124.2404604348628
Winsorized Mean ( 21 / 24 )59984034.40277782262449.9686280426.5128666863526
Winsorized Mean ( 22 / 24 )60175369.93055562202737.7335902627.3184451389386
Winsorized Mean ( 23 / 24 )60297184.95833332139258.5388344528.186020466318
Winsorized Mean ( 24 / 24 )60325929.29166671969580.9194514630.6288148386753
Trimmed Mean ( 1 / 24 )56929151.15714293532242.0138927316.1170018739469
Trimmed Mean ( 2 / 24 )57076132.27941183493090.0480093916.3397254279024
Trimmed Mean ( 3 / 24 )57232452.12121213445614.4482700916.6102310576119
Trimmed Mean ( 4 / 24 )57428389.06253400139.4684511416.8900098349966
Trimmed Mean ( 5 / 24 )57638402.90322583351444.9832537317.1980752156844
Trimmed Mean ( 6 / 24 )57860831.453313072.5565179217.4644021411992
Trimmed Mean ( 7 / 24 )58080239.79310343276701.1005164417.7252175317271
Trimmed Mean ( 8 / 24 )582801703239000.6586973117.9932566063261
Trimmed Mean ( 9 / 24 )58512378.9629633193465.7269808518.3225323098368
Trimmed Mean ( 10 / 24 )58705284.01923083150495.3849071218.6336676766665
Trimmed Mean ( 11 / 24 )58794743.123125204.8378540718.8130846361967
Trimmed Mean ( 12 / 24 )58912801.85416673094399.9039416519.0385223897931
Trimmed Mean ( 13 / 24 )59020584.23913043057169.7559760819.3056287187712
Trimmed Mean ( 14 / 24 )59094628.13636363017403.4082405619.5845964695923
Trimmed Mean ( 15 / 24 )59198151.23809522968163.9589600419.9443669745375
Trimmed Mean ( 16 / 24 )59334236.12905425.7785349920.4218729448729
Trimmed Mean ( 17 / 24 )59460768.6315792856479.246569520.8161038463656
Trimmed Mean ( 18 / 24 )59574862.22222222793804.4553833221.3239198281858
Trimmed Mean ( 19 / 24 )59785898.67647062728138.1200283121.9145424630665
Trimmed Mean ( 20 / 24 )59935199.156252664575.3019476522.493340350502
Trimmed Mean ( 21 / 24 )60066248.56666672600696.9219102123.0962124269936
Trimmed Mean ( 22 / 24 )60076315.60714292550677.277818323.5530837748821
Trimmed Mean ( 23 / 24 )60063847.23076922485215.6578014224.1684648341164
Trimmed Mean ( 24 / 24 )60033411.8752397079.7240710925.0443951747428
Median64973774.5
Midrange211983851.5
Midmean - Weighted Average at Xnp58745035.8378378
Midmean - Weighted Average at X(n+1)p59574862.2222222
Midmean - Empirical Distribution Function58745035.8378378
Midmean - Empirical Distribution Function - Averaging59574862.2222222
Midmean - Empirical Distribution Function - Interpolation59574862.2222222
Midmean - Closest Observation58745035.8378378
Midmean - True Basic - Statistics Graphics Toolkit59574862.2222222
Midmean - MS Excel (old versions)59460768.631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 61236226.1666667 & 6166783.36939057 & 9.9300109147045 \tabularnewline
Geometric Mean & 44817948.0129479 &  &  \tabularnewline
Harmonic Mean & 25561026.4747938 &  &  \tabularnewline
Quadratic Mean & 80311579.5574312 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 56790335.6527778 & 3563956.9256335 & 15.9346301983386 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 56789545.9027778 & 3563075.04858834 & 15.9383524423033 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 56709953.6111111 & 3534418.95254753 & 16.0450570157326 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 56705008.0555556 & 3513322.3371468 & 16.1399958825316 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 56711617.2916667 & 3440781.75785323 & 16.4821895960789 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 56800357.7916667 & 3395089.00313743 & 16.7301527998757 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 56991730.8888889 & 3358952.50316784 & 16.9671142521782 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 56886916.2222222 & 3343658.11438259 & 17.0133770487855 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 57258496.0972222 & 3275251.3307278 & 17.48216863849 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 58084040.2638889 & 3134605.8011121 & 18.5299345274234 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 57928979.0694444 & 3110660.42191558 & 18.6227267564523 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 58086470.2361111 & 3083583.01187296 & 18.8373298245763 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 58432346.6111111 & 3028540.88574845 & 19.2938939296078 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 58249189.4722222 & 2997875.76865065 & 19.4301545385386 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 58064110.7222222 & 2970191.72659958 & 19.5489436598414 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 58265739.1666667 & 2804991.37641004 & 20.7721633858418 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 58490973.1111111 & 2770351.60150863 & 21.1131948303093 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 57781052.3611111 & 2664298.25452304 & 21.68715618194 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 58525139.0694444 & 2543324.09274046 & 23.0112785218745 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 58843120.7361111 & 2427475.37301241 & 24.2404604348628 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 59984034.4027778 & 2262449.96862804 & 26.5128666863526 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 60175369.9305556 & 2202737.73359026 & 27.3184451389386 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 60297184.9583333 & 2139258.53883445 & 28.186020466318 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 60325929.2916667 & 1969580.91945146 & 30.6288148386753 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 56929151.1571429 & 3532242.01389273 & 16.1170018739469 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 57076132.2794118 & 3493090.04800939 & 16.3397254279024 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 57232452.1212121 & 3445614.44827009 & 16.6102310576119 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 57428389.0625 & 3400139.46845114 & 16.8900098349966 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 57638402.9032258 & 3351444.98325373 & 17.1980752156844 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 57860831.45 & 3313072.55651792 & 17.4644021411992 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 58080239.7931034 & 3276701.10051644 & 17.7252175317271 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 58280170 & 3239000.65869731 & 17.9932566063261 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 58512378.962963 & 3193465.72698085 & 18.3225323098368 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 58705284.0192308 & 3150495.38490712 & 18.6336676766665 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 58794743.12 & 3125204.83785407 & 18.8130846361967 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 58912801.8541667 & 3094399.90394165 & 19.0385223897931 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 59020584.2391304 & 3057169.75597608 & 19.3056287187712 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 59094628.1363636 & 3017403.40824056 & 19.5845964695923 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 59198151.2380952 & 2968163.95896004 & 19.9443669745375 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 59334236.1 & 2905425.77853499 & 20.4218729448729 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 59460768.631579 & 2856479.2465695 & 20.8161038463656 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 59574862.2222222 & 2793804.45538332 & 21.3239198281858 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 59785898.6764706 & 2728138.12002831 & 21.9145424630665 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 59935199.15625 & 2664575.30194765 & 22.493340350502 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 60066248.5666667 & 2600696.92191021 & 23.0962124269936 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 60076315.6071429 & 2550677.2778183 & 23.5530837748821 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 60063847.2307692 & 2485215.65780142 & 24.1684648341164 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 60033411.875 & 2397079.72407109 & 25.0443951747428 \tabularnewline
Median & 64973774.5 &  &  \tabularnewline
Midrange & 211983851.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 58745035.8378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 59574862.2222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 58745035.8378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 59574862.2222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 59574862.2222222 &  &  \tabularnewline
Midmean - Closest Observation & 58745035.8378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 59574862.2222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 59460768.631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120351&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]61236226.1666667[/C][C]6166783.36939057[/C][C]9.9300109147045[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]44817948.0129479[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]25561026.4747938[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]80311579.5574312[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]56790335.6527778[/C][C]3563956.9256335[/C][C]15.9346301983386[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]56789545.9027778[/C][C]3563075.04858834[/C][C]15.9383524423033[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]56709953.6111111[/C][C]3534418.95254753[/C][C]16.0450570157326[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]56705008.0555556[/C][C]3513322.3371468[/C][C]16.1399958825316[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]56711617.2916667[/C][C]3440781.75785323[/C][C]16.4821895960789[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]56800357.7916667[/C][C]3395089.00313743[/C][C]16.7301527998757[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]56991730.8888889[/C][C]3358952.50316784[/C][C]16.9671142521782[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]56886916.2222222[/C][C]3343658.11438259[/C][C]17.0133770487855[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]57258496.0972222[/C][C]3275251.3307278[/C][C]17.48216863849[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]58084040.2638889[/C][C]3134605.8011121[/C][C]18.5299345274234[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]57928979.0694444[/C][C]3110660.42191558[/C][C]18.6227267564523[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]58086470.2361111[/C][C]3083583.01187296[/C][C]18.8373298245763[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]58432346.6111111[/C][C]3028540.88574845[/C][C]19.2938939296078[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]58249189.4722222[/C][C]2997875.76865065[/C][C]19.4301545385386[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]58064110.7222222[/C][C]2970191.72659958[/C][C]19.5489436598414[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]58265739.1666667[/C][C]2804991.37641004[/C][C]20.7721633858418[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]58490973.1111111[/C][C]2770351.60150863[/C][C]21.1131948303093[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]57781052.3611111[/C][C]2664298.25452304[/C][C]21.68715618194[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]58525139.0694444[/C][C]2543324.09274046[/C][C]23.0112785218745[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]58843120.7361111[/C][C]2427475.37301241[/C][C]24.2404604348628[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]59984034.4027778[/C][C]2262449.96862804[/C][C]26.5128666863526[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]60175369.9305556[/C][C]2202737.73359026[/C][C]27.3184451389386[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]60297184.9583333[/C][C]2139258.53883445[/C][C]28.186020466318[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]60325929.2916667[/C][C]1969580.91945146[/C][C]30.6288148386753[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]56929151.1571429[/C][C]3532242.01389273[/C][C]16.1170018739469[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]57076132.2794118[/C][C]3493090.04800939[/C][C]16.3397254279024[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]57232452.1212121[/C][C]3445614.44827009[/C][C]16.6102310576119[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]57428389.0625[/C][C]3400139.46845114[/C][C]16.8900098349966[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]57638402.9032258[/C][C]3351444.98325373[/C][C]17.1980752156844[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]57860831.45[/C][C]3313072.55651792[/C][C]17.4644021411992[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]58080239.7931034[/C][C]3276701.10051644[/C][C]17.7252175317271[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]58280170[/C][C]3239000.65869731[/C][C]17.9932566063261[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]58512378.962963[/C][C]3193465.72698085[/C][C]18.3225323098368[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]58705284.0192308[/C][C]3150495.38490712[/C][C]18.6336676766665[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]58794743.12[/C][C]3125204.83785407[/C][C]18.8130846361967[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]58912801.8541667[/C][C]3094399.90394165[/C][C]19.0385223897931[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]59020584.2391304[/C][C]3057169.75597608[/C][C]19.3056287187712[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]59094628.1363636[/C][C]3017403.40824056[/C][C]19.5845964695923[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]59198151.2380952[/C][C]2968163.95896004[/C][C]19.9443669745375[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]59334236.1[/C][C]2905425.77853499[/C][C]20.4218729448729[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]59460768.631579[/C][C]2856479.2465695[/C][C]20.8161038463656[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]59574862.2222222[/C][C]2793804.45538332[/C][C]21.3239198281858[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]59785898.6764706[/C][C]2728138.12002831[/C][C]21.9145424630665[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]59935199.15625[/C][C]2664575.30194765[/C][C]22.493340350502[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]60066248.5666667[/C][C]2600696.92191021[/C][C]23.0962124269936[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]60076315.6071429[/C][C]2550677.2778183[/C][C]23.5530837748821[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]60063847.2307692[/C][C]2485215.65780142[/C][C]24.1684648341164[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]60033411.875[/C][C]2397079.72407109[/C][C]25.0443951747428[/C][/ROW]
[ROW][C]Median[/C][C]64973774.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]211983851.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]58745035.8378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]59574862.2222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]58745035.8378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]59574862.2222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]59574862.2222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]58745035.8378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]59574862.2222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]59460768.631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120351&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean61236226.16666676166783.369390579.9300109147045
Geometric Mean44817948.0129479
Harmonic Mean25561026.4747938
Quadratic Mean80311579.5574312
Winsorized Mean ( 1 / 24 )56790335.65277783563956.925633515.9346301983386
Winsorized Mean ( 2 / 24 )56789545.90277783563075.0485883415.9383524423033
Winsorized Mean ( 3 / 24 )56709953.61111113534418.9525475316.0450570157326
Winsorized Mean ( 4 / 24 )56705008.05555563513322.337146816.1399958825316
Winsorized Mean ( 5 / 24 )56711617.29166673440781.7578532316.4821895960789
Winsorized Mean ( 6 / 24 )56800357.79166673395089.0031374316.7301527998757
Winsorized Mean ( 7 / 24 )56991730.88888893358952.5031678416.9671142521782
Winsorized Mean ( 8 / 24 )56886916.22222223343658.1143825917.0133770487855
Winsorized Mean ( 9 / 24 )57258496.09722223275251.330727817.48216863849
Winsorized Mean ( 10 / 24 )58084040.26388893134605.801112118.5299345274234
Winsorized Mean ( 11 / 24 )57928979.06944443110660.4219155818.6227267564523
Winsorized Mean ( 12 / 24 )58086470.23611113083583.0118729618.8373298245763
Winsorized Mean ( 13 / 24 )58432346.61111113028540.8857484519.2938939296078
Winsorized Mean ( 14 / 24 )58249189.47222222997875.7686506519.4301545385386
Winsorized Mean ( 15 / 24 )58064110.72222222970191.7265995819.5489436598414
Winsorized Mean ( 16 / 24 )58265739.16666672804991.3764100420.7721633858418
Winsorized Mean ( 17 / 24 )58490973.11111112770351.6015086321.1131948303093
Winsorized Mean ( 18 / 24 )57781052.36111112664298.2545230421.68715618194
Winsorized Mean ( 19 / 24 )58525139.06944442543324.0927404623.0112785218745
Winsorized Mean ( 20 / 24 )58843120.73611112427475.3730124124.2404604348628
Winsorized Mean ( 21 / 24 )59984034.40277782262449.9686280426.5128666863526
Winsorized Mean ( 22 / 24 )60175369.93055562202737.7335902627.3184451389386
Winsorized Mean ( 23 / 24 )60297184.95833332139258.5388344528.186020466318
Winsorized Mean ( 24 / 24 )60325929.29166671969580.9194514630.6288148386753
Trimmed Mean ( 1 / 24 )56929151.15714293532242.0138927316.1170018739469
Trimmed Mean ( 2 / 24 )57076132.27941183493090.0480093916.3397254279024
Trimmed Mean ( 3 / 24 )57232452.12121213445614.4482700916.6102310576119
Trimmed Mean ( 4 / 24 )57428389.06253400139.4684511416.8900098349966
Trimmed Mean ( 5 / 24 )57638402.90322583351444.9832537317.1980752156844
Trimmed Mean ( 6 / 24 )57860831.453313072.5565179217.4644021411992
Trimmed Mean ( 7 / 24 )58080239.79310343276701.1005164417.7252175317271
Trimmed Mean ( 8 / 24 )582801703239000.6586973117.9932566063261
Trimmed Mean ( 9 / 24 )58512378.9629633193465.7269808518.3225323098368
Trimmed Mean ( 10 / 24 )58705284.01923083150495.3849071218.6336676766665
Trimmed Mean ( 11 / 24 )58794743.123125204.8378540718.8130846361967
Trimmed Mean ( 12 / 24 )58912801.85416673094399.9039416519.0385223897931
Trimmed Mean ( 13 / 24 )59020584.23913043057169.7559760819.3056287187712
Trimmed Mean ( 14 / 24 )59094628.13636363017403.4082405619.5845964695923
Trimmed Mean ( 15 / 24 )59198151.23809522968163.9589600419.9443669745375
Trimmed Mean ( 16 / 24 )59334236.12905425.7785349920.4218729448729
Trimmed Mean ( 17 / 24 )59460768.6315792856479.246569520.8161038463656
Trimmed Mean ( 18 / 24 )59574862.22222222793804.4553833221.3239198281858
Trimmed Mean ( 19 / 24 )59785898.67647062728138.1200283121.9145424630665
Trimmed Mean ( 20 / 24 )59935199.156252664575.3019476522.493340350502
Trimmed Mean ( 21 / 24 )60066248.56666672600696.9219102123.0962124269936
Trimmed Mean ( 22 / 24 )60076315.60714292550677.277818323.5530837748821
Trimmed Mean ( 23 / 24 )60063847.23076922485215.6578014224.1684648341164
Trimmed Mean ( 24 / 24 )60033411.8752397079.7240710925.0443951747428
Median64973774.5
Midrange211983851.5
Midmean - Weighted Average at Xnp58745035.8378378
Midmean - Weighted Average at X(n+1)p59574862.2222222
Midmean - Empirical Distribution Function58745035.8378378
Midmean - Empirical Distribution Function - Averaging59574862.2222222
Midmean - Empirical Distribution Function - Interpolation59574862.2222222
Midmean - Closest Observation58745035.8378378
Midmean - True Basic - Statistics Graphics Toolkit59574862.2222222
Midmean - MS Excel (old versions)59460768.631579
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')